Agricultural production is fundamentally an intertwined process of natural reproduction and economic reproduction. Climatic factors, as core natural variables, disrupt crop physiological cycles and the efficiency of production factor allocation through nonlinear pathways. Weather extremes directly destabilize the stable growth environment for crops by altering the spatiotemporal distribution of light, temperature, water, and heat resources. This triggers a cascade of effects including intensified pest and disease outbreaks, suppression of photosynthesis, and disruption of pollination processes (Lobell and Gourdji, 2012). These disturbances manifest as yield fluctuations at the micro level while escalating into regional food supply imbalances at the macro level. Within the theoretical framework of agricultural production functions, the impact of climatic shocks on output can be deconstructed into two primary pathways: technical efficiency loss and resource utilization distortion (Aragon et al., 2021). On one hand, anomalous precipitation or temperatures deviating from optimal crop growth thresholds cause soil moisture imbalances and nutrient depletion, reducing the marginal output elasticity of land (Shirley et al., 2020) drought-induced irrigation water scarcity directly reduces grai. On the other hand, catastrophic events compel farmers to adjust their strategies for factor inputs. Topographic heterogeneity plays a critical role in this process—plains areas, with their advantages in contiguous cultivation and mechanization adaptability, can buffer climatic shocks through scale economies. Conversely, hilly and mountainous regions, constrained by fragmented landholdings and ecological fragility, experience amplified effects of climatic disturbances through exacerbated soil erosion and microhabitat degradation. Consequently, theoretical models must simultaneously capture the direct biophysical effects of climatic variables and their interactive effects with topographic features to precisely quantify the net impact of extreme weather on food security.

Crop production is the result of the interaction between socioeconomic and natural factors. Therefore, when examining the impact of climate factor changes on food security, the primary consideration is how climate factors affect crop yields and agricultural production efficiency. During the derivation of the production function, it is first necessary to separate the economic yield of food crops to obtain the yield determined solely by natural factors under climate variables, thus identifying the “fluctuating yield” influenced by climate. Therefore, the total yield of food crops is defined as Equation (1): (1) Y = Y i + Y c + ε

In the above formula, Y represents the total grain yield in a given region, Y_i denotes the economic yield resulting from social factors in that region, Y_c signifies the fluctuating yield affected by climate, and ε represents the random error.

To accurately investigate the fluctuating yield impacted by climate, this study applies the Cobb–Douglas production function to calculate socioeconomic yield and thus assess the influence of various socioeconomic factors on yield as Equation (2): (2) Y i = K 1 α 1 K 2 α 2

Here, K₁ and K₂ represent two primary socioeconomic factors under simplified expressions, α₁ and α₂ are the corresponding elasticity coefficients of these factors, satisfying α 1 + α 2 = 1 , which aligns with the assumption of constant returns to scale. Under constant factor inputs, grain production efficiency can be represented as the ratio of actual grain output to optimal output. Within a fixed period, if the optimal yield from arable land remains constant, production efficiency can thus represent actual grain output in calculations.

The stochastic frontier approach (SFA) model, introduced in 1977, has since undergone extensive research and development, gaining widespread attention for its application in measuring resource use efficiency and analyzing utilization patterns. Analyzing grain production reveals that primary constraints on output include arable land conditions and capital investment. This paper constructs a stochastic frontier production function (SFA) to calculate grain production efficiency. This paper constructs a stochastic frontier production function to calculate grain production expressed as Equation (3): (3) ln ( Y i ) = ln ( f ( K 1 , K 2 ) ) + v − u

Here, v represents a random error term following a normal distribution N ( 0 , σ v 2 ) , u is a random variable assumed to be non-negative due to technical inefficiency, following a truncated normal distribution N + ( 0 , σ u 2 ) . In the specified model, agricultural production efficiency (APE) with regard to socioeconomic factors can be defined as Equation (4): (4) APE = Y i exp ( ln ( f ( K 1 , K 2 ) ) + v )

To introduce the impact of climate factors on yield variability Y_c, this paper selects typical climate variables C, including precipitation P, temperature T, and humidity H, to examine the impact of extreme weather on agricultural production efficiency, assuming that (5) Y c = g ( C ) = g ( T , P , H )

In Equation (5), g ( · ) represents a function of climate variables. At this point, Y_c is a function of T, P and H, as these climate variables influence the variability of crop yields. To incorporate the impact of climate factors on production efficiency into the model, climate variables C are introduced as additional input variables, assuming that the production function becomes Equation (6): (6) ln ( Y ) = ln ( f ( K 1 , K 2 ) ) + ln ( g ( C ) ) + v − u

At this point, ln ( g ( C ) ) reflects the direct impact of climate factors on crop yield. Following the previous assumption, let g ( C ) = T β 1 · P β 2 · H β 3 , where β₁, β₂ and β₃ are elasticity coefficients representing the influence of temperature, precipitation, and humidity on crop yield, respectively. In summary, the production function is expressed as Equation (7): (7) ln ( Y ) = α 1 ln ( K 1 ) + α 2 ln ( K 2 ) + β 1 ln ( T ) + β 2 ln ( P ) + β 3 ln ( H ) + v − u

At this point, in terms of total output, agricultural production efficiency (APE) can be redefined as Equation (8): (8) APE = Y exp ( α 1 ln ( K 1 ) + α 2 ln ( K 2 ) + β 1 ln ( T ) + β 2 ln ( P ) + β 3 ln ( H ) + v )

To explain the impact of major socioeconomic factors on agricultural production efficiency under extreme weather conditions, this paper introduces a terrain impact coefficient G to differentiate the productive effects of various terrains. Intuitively, plains are more suitable for mechanized operations, making them more favorable for cultivation compared to hilly or mountainous areas. Thus, we assume that if the terrain is conducive to cultivation G = G 1 > 1 , indicating that this terrain enhances agricultural production efficiency. Conversely G = G 2 < 1 suggests that such terrain conditions constrain output and production efficiency. Based on the original production model, this paper defines the adjusted crop yield Y as Equation (9): (9) Y = G · f ( K 1 , K 2 ) · g ( C ) · e v − u

At this point, agricultural production efficiency is expressed as Equation (10): (10) APE = G · f ( K 1 , K 2 ) · g ( C ) · e v − u exp ( α 1 ln ( K 1 ) + α 2 ln ( K 2 ) + β 1 ln ( T ) + β 2 ln ( P ) + β 3 ln ( H ) + v )

If G = G 1 > 1 : Under these terrain conditions, favorable natural factors such as soil quality, moisture, and slope enhance crop growth, increasing yield per unit area and production efficiency. G 1 > 1 represents a positive impact of terrain on output. The opposite holds for unfavorable terrain. The terrain coefficient G directly multiplies the original output, either amplifying or reducing the final crop yield. Thus, terrain conditions alter the efficiency value, with favorable terrain increasing efficiency and unfavorable terrain reducing it.

Food security is fundamentally a function of supply stability and access reliability. Extreme weather indirectly threatens food security by disrupting the dual pathways through which rural households obtain food—subsistence production and market procurement. Subsistence production, serving as the first line of defense against risk, sees its output elasticity significantly suppressed by climate shocks: drought-induced irrigation water scarcity directly reduces grain setting rates, while waterlogging from heavy rainfall accelerates root rot and grain mold, leading to contraction in household grain reserves (Wheeler and von Braun, 2013). As the subsistence production gap widens, households increasingly rely on market procurement to meet consumption needs. However, extreme weather simultaneously distorts the agricultural supply chain—floods damaging transport networks increase logistics costs, while high temperatures accelerate the spoilage of perishables, exacerbating supply losses. This manifests as heightened market price volatility and supply uncertainty. These dual pressures create a negative cycle of “subsistence decline–market failure”: weakened self-sufficiency forces greater market dependence, while market failure increases the cost and risk of food access. Theoretical models must specifically identify the differing substitution elasticities of these two mediating pathways. In plains with developed infrastructure, market mechanisms can partially offset production losses; in high-transaction-cost mountainous areas, however, the combined effect of diminished subsistence output and obstructed procurement causes a sharp decline in food security levels. Consequently, the mode of food sourcing acts as the critical nexus transmitting climate shocks to food security outcomes, with transmission efficiency profoundly constrained by regional market development and logistical resilience.

To quantify the complementary relationship between self-sufficient food production and external market purchases in ensuring food security, this paper develops a corresponding mediation effect model. Self-sufficiency in production and external market purchases are treated as two key variables affecting food security, with consideration given to the impact of extreme weather on both. The specific modeling approach is as follows:

Food security level is represented y, y a function of the quantity of food produced for self-sufficiency Q₁ and the quantity purchased from external markets Q₂, both influenced by extreme weather C. The mediation effect model can be constructed as Equation (11): (11) y = φ + τ 1 Q 1 + τ 2 Q 2 + γC + δ ( Q 1 · C ) + θ ( Q 2 · C ) + ∈

Here, Q₁ denotes the quantity of food produced by farmers for self-sufficiency, which can reduce dependency on the external market. Q₂ represents the quantity of food purchased from the external market, which can supplement supply when self-sufficient production is insufficient. C (as previously defined) represents the variable for extreme weather intensity. φ is a constant term representing the baseline level of food security. τ₁ and τ₂ are the direct impact coefficients of self-sufficient production Q₁ and external market purchases Q₂ on food security level. γ is the direct impact coefficient of extreme weather on food security. δ is the coefficient of the interaction term Q 1 × C , measuring the compensatory effect of self-sufficient production on food security under extreme weather. θ is the coefficient of the interaction term Q 2 × C , indicating the effect of extreme weather on dependency on external markets. ϵ is the error term, capturing unexplained random fluctuations within the model.

In this framework, the impact coefficient τ₁ of Q₁ on y indicates how an increase in self-sufficient production enhances food security. If τ 1 > 0 , it suggests that increasing the self-sufficient production Q₁ helps to improve food security levels, as self-sufficiency can stabilize food supply. The impact coefficient τ₂ of Q₂ on y represents the supplementary effect of external market purchases. If τ 2 > 0 , external market purchases Q₂ can supplement supply, mitigating shortages and strengthening food security. Additionally, extreme weather C impacts food security through the direct coefficient γ; If γ < 0 , extreme weather has a negative effect on food security. The interaction terms Q 1 × C and Q 2 × C examine the mediating roles of self-sufficient production and external market purchases on food security under extreme weather conditions. If δ > 0 , it suggests that self-sufficient production can mitigate the impact of extreme weather on food security, reducing dependence on the external market. Conversely, if θ < 0 , it implies that external market purchases may be adversely affected by extreme weather, thereby reducing food security levels.

Digital economy mitigates the negative impact of extreme weather on food security through four-dimensional restructuring. Digital acceptance determines the breadth of farmers’ application of digital tools, with high-adoption groups proactively leveraging digital technologies to avoid planting risks and reduce production-side vulnerabilities. Digital finance innovates risk-dispersing instruments, converting physical losses into actuarial payouts to alleviate post-disaster capital constraints hindering grain reproduction. Digital production technologies optimize resource allocation by dynamically adjusting water, fertilizer, and pesticide inputs in real time, thereby suppressing yield volatility (Yu et al., 2025). Digital infrastructure underpins this ecosystem: logistics big data platforms dynamically route shipments around disaster-affected routes, while e-commerce markets bridge information gaps by connecting oversupplied regions with cross-regional demand (Giacalone, 2025). Crucially, these four dimensions synergistically form an “early warning-buffer-adaptation-recovery” cycle. Digital economy not only shortens the time lag between climate shocks and responsive decision-making but also reduces climate sensitivity per unit output through precision resource allocation. Theoretical models must elucidate how digital economy reshapes the response function of “climate shock-food security” by reducing information asymmetry, enhancing factor mobility, and strengthening risk dispersion capabilities—fundamentally shifting the marginal effect curve of climate impacts downward through reduced systemic vulnerability and heightened adaptive capacity.

To further analyze the moderating effect of the digital economy on the relationship between food security and extreme weather, this paper introduces the moderating variable T to build an econometric model. The digital economy can mitigate the negative impact of extreme weather on food security by enhancing information transmission efficiency, optimizing supply chain management, and promoting precision agriculture. Extending the discussion above, the econometric model introduces a digital economy moderation variable, where food security level y has a direct relationship with Q, and extreme weather C and the digital economy T have a moderating effect on y. The model is constructed as Equation (12): (12) y = φ + τQ + γC + ϑ ( T · C ) + ∈

In addition to the variables defined in the previous model, Q represents the total quantity of food (regardless of source), and τ is the direct impact coefficient of the total food quantity Q on food security. ϑ is the interaction coefficient between extreme weather and the digital economy, measuring the moderating effect of the digital economy on food security under extreme weather conditions.

If τ > 0 , this indicates that increasing the food supply Q can directly enhance food security levels. The interaction term T × C has a coefficient ϑ, representing the moderating effect of the digital economy on food security under extreme weather conditions. If ϑ > 0 this suggests that the digital economy can exert a positive moderating effect on food security during extreme weather. Advances in the digital economy, such as supply chain optimization, market information transmission, and precision agriculture technology, can mitigate the negative impact of extreme weather on food security.

The data for this study primarily come from two sources: first, micro-level survey data from farmers. This survey was led by the research team in collaboration with the Rural Revitalization Institute of Sichuan Open University, focusing on agricultural production, the digital economy, and land use. The survey was conducted among farmers in Sichuan Province in the summer of 2024. Based on the geographical characteristics, the research team divided Sichuan Province into five regions: Eastern Sichuan, Western Sichuan, Southern Sichuan, Northern Sichuan, and Central Sichuan. Two prefecture-level cities were randomly selected from each region. Employing a combined stratified and random sampling approach, five distinct villages were chosen per city based on two criteria: proximity to urban centers (categorized as near-village [<5 km], medium-distance village [5–10 km], and remote village [>10 km]) and economic development level (high, medium, low) determined by tertile-based pairing of village-level GDP. Using official rosters provided by village committees, 25 farming households were then randomly sampled per village for in-person household surveys. A total of 1,250 farmer questionnaires were collected in this survey. After excluding irrelevant, incomplete, or invalid responses and conducting several follow-up phone interviews, 1,066 valid questionnaires were obtained, yielding an effective response rate of 85.28%. Sichuan Province is located in the southwest interior of China, spanning the first and second steps of the Chinese mainland’s topography, characterized by significant elevation differences, with higher elevations in the west and lower elevations in the east. The region features diverse and complex terrain, including plateaus, mountains, hills, and plains. Given the varied natural resource endowments, the development of the digital economy and the manifestation of extreme weather exhibit significant heterogeneity, making this study both forward-looking and highly representative. The second source is climate data. The extreme weather indicators used in this study were obtained and further processed from the China Meteorological Science Data Center and the U.S. National Oceanic and Atmospheric Administration (Figure 1).

This paper constructs an equation to examine the impact of extreme weather on farmers’ food security. Based on the nature of the dependent variable, the Ordinary Least Squares (OLS) model is used for econometric analysis, and the specific expression is shown in Equation (13): (13) Y i = α 0 + α 1 CPRI i + α 2 X i + μ i

In this equation, the dependent variable Y_i represents the farmers’ food security index, the independent variable CPRI i represents the Climate Physical Risk Index, and X_i represents control variables that may affect the dependent variable. α₀, α₁ and α₂ are the parameters to be estimated; μ_i represents the error term.

Before performing the regression analysis, this study uses the Variance Inflation Factor (VIF) to test for multicollinearity among the variables. The results indicate that all VIF values are below 10, indicating no multicollinearity. Table 5 presents the impact of extreme weather on farmers’ food security. For every one-unit increase in the extreme climate risk index, the household food security index increases by 15.2%, suggesting that an increase in extreme weather events is associated with a higher food security index for farmers. Additionally, this study employs extreme weather data from 2014 and the slope of the study area as instrumental variables to address endogeneity. First, the extreme weather events of 2014 are past natural occurrences, unaffected by current farmer behavior or food security conditions, thereby possessing exogeneity. Additionally, the climate system exhibits continuity, and there is typically a strong correlation between past extreme weather events and current climate conditions. Second, the slope of the study area, as a geographic feature, is a stable and exogenous variable that cannot be influenced by individual behavior. Slope affects local climate conditions, such as precipitation patterns, soil water retention, and erosion risk, all of which are closely linked to the frequency and intensity of extreme weather events. However, this natural feature remains unchanged by farmers’ decisions or food production activities. The chosen instrumental variables meet the assumptions of relevance and exogeneity, and pass the relevant tests, fulfilling the selection requirements. Additionally, when the 2SLS model is replaced with the LIML model for regression, the results remain consistent—after accounting for endogeneity and robustness, more extreme weather events still correspond to a higher food security index for farmers.

The control variables revealed significant variations in household food security levels. An increase in female-headed households, younger age demographics, and higher education attainment positively enhanced food security. At the household level, expanded cultivated land area and greater non-agricultural employment participation similarly improved food security outcomes. Village-level proximity to townships and location in plains further amplified these positive effects. Human capital (gender, age, education) and livelihood strategies (cultivated land scale, non-agricultural employment) constituted foundational capacities for risk resilience, whereas geographical positioning (urban proximity, plain advantages) amplified protective effects through enhanced resource accessibility (Table 6).

However, this phenomenon is clearly counterintuitive. Typically, climatic shocks disrupt the natural growing conditions for crops, increasing uncertainty and risk in agricultural production, which in turn reduces crop yields and quality, weakening the stability of the food supply (Wineman et al., 2017; Chriest and Niles, 2018). Research also confirms that, from a macro perspective, climate change negatively impacts the stability of food security (Hasegawa et al., 2021). Why, then, do conclusions from the micro perspective completely contradict those from the macro perspective? By comparing and reanalyzing the original data, significant differences between extreme weather events and farmers’ food security indices were observed across different topographical conditions (Table 6): In plain areas, despite the higher frequency of extreme weather events, farmers’ food security indices are also higher. In non-plain areas (mainly hills and mountains), although extreme weather events occur less frequently, farmers’ food security indices are lower.

Furthermore, Table 7 demonstrates the differences in extreme weather and farmers’ food security across topographies: a one-unit increase in the extreme weather index raised the food security index by 28.2% in plain areas but reduced it by 9.7% in non-plain areas. A possible explanation is that plains feature flat terrain, better transportation and infrastructure, and more advanced digital economic development, which makes it easier for farmers to access disaster prevention information and technical support, thereby enhancing their ability to cope with extreme weather. Additionally, plain areas have higher levels of agricultural mechanization and production efficiency, so even though climatic shocks occur more frequently, farmers’ food security can still be maintained. In contrast, non-plain areas are characterized by more complex terrain, poor transportation networks, underdeveloped infrastructure, and lagging digital economic development. Farmers in these regions have limited access to information and technical support, making them more vulnerable to extreme weather despite relatively stable climatic conditions.

Food sourcing methods (self-sufficiency and external purchasing) serve as complementary mediators between extreme weather and farmers’ food security. As shown in Table 8, extreme weather events have significantly different effects on farmers’ food supply sources across various topographical conditions. In plain areas, an increase in weather extremes leads farmers to rely more on external food purchases, while their level of self-sufficiency remains largely unaffected. In contrast, in non-plain areas (such as mountainous and hilly regions), extreme weather significantly reduces farmers’ self-sufficiency, yet has no significant effect on external food purchases. The core driving factors behind this phenomenon can be attributed to the imbalances in agricultural production efficiency and the allocation of economic resources (Table 9).

First, due to favorable terrain conditions, plain areas have higher levels of agricultural mechanization, with production efficiency far surpassing that of non-plain areas. The agricultural infrastructure in these regions is more advanced, and farmers possess greater resilience to climatic shocks. The well-developed transportation networks in plain areas enable farmers to swiftly compensate for production losses through the market, while the ease of external food purchases further diversifies their supply structure. Therefore, although extreme weather increases their reliance on external food sources, the availability of economic resources ensures that their self-sufficiency remains largely unaffected (Table 9).

In contrast, in non-plain areas, complex terrain constrains the development of agricultural mechanization and large-scale production, leading to lower production efficiency for farmers. Moreover, traditional small-scale farming methods expose them to greater production risks. Additionally, the relatively underdeveloped transportation and market infrastructure in non-plain areas limits access to external food sources, further exacerbating farmers’ difficulties in coping with extreme weather. The low production efficiency also results in generally low household incomes for farmers, leaving them without sufficient economic resources to purchase food from the market.

In summary, food sourcing methods (self-sufficiency and external purchasing) act as mediators between extreme weather and food security, further highlighting the deeper influence of agricultural production efficiency and farmers’ income on this relationship. However, with the rapid development of the digital economy, its application in agriculture has profoundly impacted traditional production methods and farmers’ livelihoods. Therefore, it is necessary to further explore the moderating role of the digital economy in the relationship between extreme weather and food security, in order to fully understand its mechanisms in mitigating the impacts of extreme weather.

In plain areas, the digital economy demonstrates a clear moderating effect on mitigating the impact of extreme weather on farmers’ food security. Data in Table 10 indicate that the digital economy amplifies the positive impact of extreme weather on farmers’ food security, a one-unit increase in the extreme weather index amplified the food security improvement in plain areas from 28.2 to 68.9%. Moreover, plain areas facilitate mechanized operations and the rapid dissemination of information technology, enabling farmers to more fully utilize the production tools and financial services enabled by the digital economy, effectively mitigating climate risks.

In contrast, Table 11 presents different dynamics for non-plain areas (such as mountainous and hilly regions). In non-plain areas, extreme weather no longer exerted a significant effect. Although the digital economy has mitigated the negative impact of extreme weather on food security to some extent, particularly in areas like digital acceptance, digital production, and digital finance, the moderating effect of digital infrastructure has had a negative impact. The complexity of non-plain terrains significantly limits the expansion and maintenance of infrastructure, not only increasing costs but also making it more vulnerable to damage from natural disasters. The fragility of digital infrastructure significantly amplifies the uncertainty surrounding food security during weather extremes.

From the previous analysis, it is clear that digital production and digital finance play crucial roles in moderating the impact of extreme weather on farmers’ food security. Digital finance not only helps farmers diversify risk by offering a range of financial tools, but also provides timely financial support during climatic shocks, reducing the economic pressure caused by climate fluctuations. At the same time, digital production, through the use of precision agriculture technologies, employs data-driven management and predictive models to increase production efficiency, reduce resource waste, and help farmers optimize production decisions, further enhancing their ability to cope with uncertainties. In this context, how does the involvement of the digital economy affect specific indicators such as agricultural insurance, production efficiency, and farmers’ income?

It is evident from the (Table 12) that the digital economy has a significantly positive impact on farmers’ adoption of agricultural insurance, improvement of production efficiency, and income growth, with an even greater effect in non-plain areas. The key reason behind this is that the complex terrain and higher natural risks in non-plain areas cause farmers to rely more heavily on digital technologies. The digital economy enhances farmers’ ability to access insurance and improve production efficiency by optimizing information transmission, risk management, and financial services, thereby significantly boosting their income levels. The digital economy plays a more significant moderating and facilitating role in areas with less favorable resources and conditions (Table 12).

Extreme weather is primarily categorized into extreme low temperature (LTD), extreme high temperature (HTD), extreme rainfall (ERD), and extreme drought (EDD). These different types of extreme weather events show significant heterogeneity across various topographical features. As shown in Table 13, extreme weather events are significantly more frequent in plain areas than in non-plain areas, with extreme high temperatures and droughts being the most common. How, then, do different types of extreme climate affect farmers’ food security across various topographies? Further analysis is needed to explore this.

The estimation results in Table 14 reveal the significant impact of extreme weather on farmers’ food security across various topographies. In plain regions, a one-unit increase in HTD and EED raises the household food security index by 30.2 and 33.0%, respectively. Moderate high temperatures and droughts can enhance crop photosynthesis and water use efficiency, optimizing the growing environment, especially for heat- and drought-resistant crops. In contrast, a one-unit increase in LTD and RED reduces the index by 4.5 and 7.4%, respectively. Low temperatures not only limit normal crop growth but also disrupt critical processes like pollination, leading to reduced yields. Excessive rainfall oversaturates the soil, increasing the risk of disease and negatively impacting harvests. Although irrigation systems can mitigate the effects of excessive rainfall, the damage caused by low temperatures is difficult to address through technological means, making its negative impact on food security more challenging.

In non-plain areas, only LTD has a significant negative impact on farmers’ food security, a one-unit increase in LTD reduces the index by 7.1%. In mountainous and hilly regions, the higher elevation and greater temperature variations exacerbate the inhibitory effect of low temperatures on crop growth. As for other types of extreme weather, their impact on food security in non-plain areas is not significant, possibly due to the relatively stable climate in these regions and the more dispersed nature of crop cultivation, which limits the impact of extreme weather on crop growth.